#### Answer

Using Jefferson's method, each clinic is apportioned the following number of doctors:
Clinic A is apportioned 2 doctors.
Clinic B is apportioned 3 doctors.
Clinic C is apportioned 5 doctors.

#### Work Step by Step

We can find the total patient load.
total load = 119 + 165 + 216 = 500
We can find the standard divisor.
$standard~divisor = \frac{total~load}{number~of~ doctors}$
$standard~divisor = \frac{500}{10}$
$standard~divisor = 50$
The standard divisor is 50.
We can find the standard quota for each clinic.
Clinic A:
$standard~quota = \frac{patient~load}{standard~divisor}$
$standard~quota = \frac{119}{50}$
$standard~quota = 2.38$
Clinic B:
$standard~quota = \frac{patient~load}{standard~divisor}$
$standard~quota = \frac{165}{50}$
$standard~quota = 3.30$
Clinic C:
$standard~quota = \frac{patient~load}{standard~divisor}$
$standard~quota = \frac{216}{50}$
$standard~quota = 4.32$
If each clinic is apportioned its lower quota, the number of doctors apportioned is 2 + 3 + 4, which is 9 doctors. Since there are a total of 10 doctors available, there is one surplus doctor. To obtain a sum of 10 doctors, we need to find a modified divisor that is slightly less than the standard divisor.
Let's choose a modified divisor of 43. Note that it may require a bit of trial-and-error to find a modified divisor that works. We can find the modified quota for each clinic.
Clinic A:
$modified~quota = \frac{patient~load}{modified~divisor}$
$modified~quota = \frac{119}{43}$
$modified~quota = 2.77$
Clinic B:
$modified~quota = \frac{patient~load}{modified~divisor}$
$modified~quota = \frac{165}{43}$
$modified~quota = 3.84$
Clinic C:
$modified~quota = \frac{patient~load}{modified~divisor}$
$modified~quota = \frac{216}{43}$
$modified~quota = 5.02$
Using Jefferson's method, the modified quota is rounded down to the nearest whole number. Each clinic is apportioned the following number of doctors:
Clinic A is apportioned 2 doctors.
Clinic B is apportioned 3 doctors.
Clinic C is apportioned 5 doctors.
Note that the total number of doctors apportioned is 10, so using a modified divisor of 43 is acceptable.